Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem

Author:

Barbieri Giuseppina1,Boccuto Antonio2,Vitale Gaetano1

Affiliation:

1. Department of Mathematics , University of Salerno , Via Giovanni Paolo II 132, , Fisciano , Italy

2. Department of Mathematics and Computer Sciences , University of Perugia , Via Vanvitelli 1, , Perugia , Italy

Abstract

Abstract We present the algebraic structures behind the approaches used to work with pairwise comparison matrices and, in general, the representation of preferences. We obtain a general definition of consistency and a universal decomposition in the space of PCMs, which allow us to define a consistency index. Also Arrow’s theorem, which is presented in a general form, is relevant. All the presented results can be seen in the main formulations of PCMs, i.e., multiplicative, additive and fuzzy approach, by the fact that each of them is a particular interpretation of the more general algebraic structure needed to deal with these theories.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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